To find the measure of two supplementary angles with a ratio of 3:4, follow these steps:

### Step 1: Let the angles be represented as:
- The first angle = \( 3x \)
- The second angle = \( 4x \)

### Step 2: Use the fact that the sum of supplementary angles is 180°:
\[
3x + 4x = 180°
\]

### Step 3: Simplify and solve for \( x \):
\[
7x = 180°
\]
\[
x = \frac{180°}{7} = 25.71°
\]

### Step 4: Now find the two angles:
- First angle = \( 3x = 3 \times 25.71° = 77.14° \)
- Second angle = \( 4x = 4 \times 25.71° = 102.86° \)

Thus, the two supplementary angles are approximately **77.14°** and **102.86°**.

Would you like more details or have any questions?

Here are some related questions to explore:
1. What happens if the ratio of the angles is different, like 2:3?
2. How would you find the angles if they were complementary instead of supplementary?
3. Can you use this method to solve for angles in a triangle?
4. What is the relationship between the angles in a linear pair?
5. How can you check your work to ensure these angles are correct?

**Tip:** Always double-check if angles add up to 180° when working with supplementary angles.

Learn how to find the measures of two supplementary angles in a 3:4 ratio. This step-by-step solution explains the relationship between supplementary angles and how to use algebra to solve for the angles. Suitable for students in Grades 6-8.

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